Limited memory restarted ℓp-ℓq minimization methods using generalized Krylov subspaces

Abstract Regularization of certain linear discrete ill-posed problems, as well regression can be formulated large-scale, possibly nonconvex, minimization whose objective function is the sum p th power ℓ -norm a fidelity term and q regularization term, with 0 < , ≤ 2. We describe new restarted iterative solution methods that require less computer storage execution time than described by Huang et al. (BIT Numer. Math. 57 ,351–378, 14). The reduction in achieved periodic restarts method. Computed examples illustrate restarting does not reduce quality computed solutions.